June 1: Sam DeHority

Title: Geometric Lie Algebra Actions on Moduli Spaces for K3 Surfaces

Abstract:

It is well known that various Lie algebras act on the cohomologies of moduli spaces of sheaves on surfaces. The situation is best understood when the surface is an ADE surface, and Lagrangian correspondences between Nakajima quiver varieties give representations of affine Lie algebras on birational models of moduli spaces of torsion free sheaves on the surface. It is possible to extend some of these results to the case of some K3 surfaces which have -2 curves arranged according to a Lorentzian root system and this is related to the birational geometry of the Hilbert scheme of points on K3 surfaces provided by variation of Bridgeland stability conditions.